Problem: Simplify the following expression: $ y = \dfrac{7z + 5}{z + 9} + 4 $
Answer: In order to add expressions, they must have a common denominator. Multiply the second expression by $\dfrac{z + 9}{z + 9}$ $ \dfrac{4}{1} \times \dfrac{z + 9}{z + 9} = \dfrac{4z + 36}{z + 9} $ Therefore $ y = \dfrac{7z + 5}{z + 9} + \dfrac{4z + 36}{z + 9} $ Now the expressions have the same denominator we can simply add the numerators: $y = \dfrac{7z + 5 + 4z + 36}{z + 9} $ $y = \dfrac{11z + 41}{z + 9}$